The Viking Gas Chromatograph Mass Spectrometer failed to detect organic compounds on Mars, and both the Viking Labeled Release and the Viking Gas Exchange experiments indicated a reactive soil surface. These results have led to the widespread belief that there are oxidants in the martian soil. Since H2O2 is produced by photochemical processes in the atmosphere of Mars, and has been shown in the laboratory to reproduce closely the Viking LR results, it is a likely candidate for a martian soil oxidant. Here, we report on the results of a coupled soil/atmosphere transport model for H202 on Mars. Upon diffusing into the soil, its concentration is determined by the extent to which it is adsorbed and by the rate at which it is catalytically destroyed. An analytical model for calculating the distribution of H202 in the martian atmosphere and soil is developed. The concentration of H202 in the soil is shown to go to zero at a finite depth, a consequence of the nonlinear soil diffusion equation. The model is parameterized in terms of an unknown quantity, the lifetime of H202 against heterogeneous catalytic destruction in the soil. Calculated concentrations are compared with a H202 concentration of 30 nmoles/cu cm, inferred from the Viking Labeled Release experiment. A significant result of this model is that for a wide range of H202 lifetimes (up to 105 years), the extinction depth was found to be less than 3 m. The maximum possible concentration in the top 4 cm is calculated to be approx. 240 nmoles/cu cm, achieved with lifetimes of greater than 1000 years. Concentrations higher than 30 nmoles/cu cm require lifetimes of greater than 4.3 terrestrial years. For a wide range of H202 lifetimes, it was found that the atmospheric concentration is only weakly coupled with soil loss processes. Losses to the soil become significant only when lifetimes are less than a few hours. If there are depths below which H202 is not transported, it is plausible that organic compounds, protected from an oxidizing environment, may still exist. They would have been deposited by meteors, or be the organic remains of past life.